In recent years, wireless systems have been used as means for transmitting information between devices by mobile electronic devices, household electric appliances, and peripheral devices for personal computers. The wireless systems for use by the electronic devices are fabricated as integrated semiconductor circuits having reduced size, weight, and cost. Generally, a wireless system requires a filter having a sharp cutoff frequency for separating a certain frequency component. However, since components used in integrated semiconductor circuits have large production tolerances, it has been difficult to produce filter circuits with sharp cutoff frequencies as integrated semiconductor circuits. For this reason, Gm-C filters comprising an operational transconductance amplifier (OTA) and capacitor have been used.
There are known a wireless system manufactured as an integrated semiconductor circuit and Gm-C filters used in such a wireless system, which have the structure disclosed in U.S. Pat. No. 6,400,218B1 as shown in FIGS. 1 and 2.
In the structure shown in FIG. 1, an RF signal input from antenna 104 is amplified by low-noise amplifier 106, and separated into I/Q baseband signals by local oscillator 101 and mixers 108, 109. The separated I/Q baseband signals are filtered by Gm-C filters 112, 113 to produce desired baseband signals. The signals input to Gm-C filters 112, 113 are limited in amplitude by amplitude limiting circuits 110, 111, so that the signals in required bands will not be saturated by Gm-C filters 112, 113.
Gm-C filters 112, 113 are constructed of OTAs 203 through 205, as shown in FIG. 2a, and their equivalent circuit is shown in FIG. 2b. 
In FIGS. 2a and 2b, capacitor 206 shown in FIG. 2a is the same as capacitor 210 shown in FIG. 2b, and capacitor 208 shown in FIG. 2a is the same as capacitor 211 shown in FIG. 2b. A circuit made up of OTAs 201 through 204 and capacitor 207 shown in FIG. 2a is equivalent to variable inductor 212 and variable inductor 213 shown in FIG. 2b. OTA 205 with its output terminals connected to inverting input terminals shown in FIG. 2a is equivalent to variable resistor 214 shown in FIG. 2b. 
The basic principles of a Gm-C filter will be described below with reference to FIG. 3. In FIG. 3, OTAs and a capacitor make up a low-pass filter of the first order. OTA 301 and OTA 302 have their mutual conductances Gm1, Gm2 controlled by respective Gm control signals 303, 304 which are supplied from an external source. At this time, if (Gm of OTA)>>(1/OTA output resistance) and CL>>(OTA output and input capacitances), then the relationship between input Vin and output Vout is expressed as Vout/Vin=Gm2/(sCL+Gm1) where s represents the Laplace operator. Based on this relationship, cutoff frequency ωP is expressed as Gm1/CL.
Generally, the capacitance of capacitor CL fabricated as an integrated semiconductor circuit varies due to production tolerances and temperature fluctuations. However, even when capacitor CL varies, cutoff frequency ωP can be kept constant by controlling mutual conductance Gm1 of OTA 301 with Gm control signal 303 supplied from a replica circuit, not shown. Based on this principle, OTAs and capacitors may be combined as shown in FIG. 2a to provide a filter of high order having the same function as shown in FIG. 2b. 
An OTA of the related art whose mutual conductance Gm can be controlled will be described below.
A degenerated differential OTA introduced in Bran Nauta, “Analog CMOS Filters for Very High Frequencies”, Kluwer Academic Publishers, 1993, pp. 87-88, and OTA disclosed in JP-A No. 2001-292051 are known as OTAs whose mutual conductance Gm can be controlled.
FIGS. 4a and 4b show such OTAs. Operation of the OTA shown in FIG. 4a will first be described below. Current sources 404, 405, 406, 407 supply the same current value. The resistive component of variable resistor 403 that is connected to the sources of input transistors 401, 402 has its resistance value variable dependent on mutual conductance control signal 408 supplied from an external circuit.
When the mutual conductances of input transistors 401, 402 are sufficiently large, a current of ΔV/R/2 flows from the outputs where R represents the resistive component of variable resistor 403 and ΔV the voltage of the differential component between input voltage signals. Therefore, any desired mutual conductance Gm can be achieved by controlling the resistance value of variable resistor 403 with control signal 408.
Operation of the OTA shown in FIG. 4b will be described below. OTA 411 comprises at least low-level OTAs 412 connected parallel to each other. OTAs 12 have their mutual conductances Gm selectively changeable to positive or negative values or can selectively switch into or out of operation based on control signal 413 from an external circuit. When OTAs 412 have their mutual conductances Gm selectively changed to positive or negative values or when they selectively switch into or out of operation, output currents from parallel-connected OTAs 12 are added or subtracted, with the result that the mutual conductance Gm of OTA 411 is variable.
As shown in FIG. 5a, a wireless system may have signal Pb that has a large amplitude appearing outside the required signal band due to a signal from another wireless system. When such a signal is input to a filter, if the filter comprises passive elements only as shown in FIG. 2b, then the filter is not adversely affected by signal Pb. However, if the filter comprises a Gm-C filter as shown in FIG. 2a, then some of the OTAs of the Gm-C filter may have their signals saturated or distorted due to a limited power supply voltage. This problem manifests itself especially when the circuit requires a relatively large amplitude in order to obtain sharp cutoff characteristics if the filter is a filter of a high order.
A process of improving such adverse effects due to signal Pb is disclosed in T. Hanusch, “Analog Baseband-IC for Dual Mode Direct Conversion Receiver”, ESSCIRC96, proceeding, September 1996, pp. 244-246. The process will be described below with reference to FIG. 6.
FIG. 6 shows circuit blocks around filters. In this example, low-pass filter 601 of the first order comprising passive elements, in addition to a semiconductor chip, is inserted for removing signal Pb that has a large amplitude appearing outside the band as shown in FIG. 5a. A signal output from low-pass filter 601 of the first order is amplified by gain control amplifier 602, and input to filter 603 of the high order for extracting a signal in a required band. Gain control amplifier 602 is placed in the front stage of filter 603 and gain control amplifier 604 is placed in the front stage of filter 605 for the following reasons:
Generally, it is known that since a filter fabricated as an integrated semiconductor circuit, e.g., a Gm-C filter, is made up of many parts, as shown in FIGS. 2(a) and 2(b), the semiconductor components of the circuit produce a large amount of noise, which lowers NF. NF represents the ratio of an output signal/noise ratio to an input signal/noise ratio, and serves as a parameter indicating that the amount of noise generated in the system is larger as NF is greater. There is known a process of improving NF by reducing noise generated by the components of the circuit and a process of improving NF by amplifying a signal input to the system in a front stage.
The process of reducing noise generated by the components of the circuit suffers limitations due to specifications including the frequency band and current consumption. The process of amplifying a signal input to the system in a front stage is an effective process of improving NF, and has amplifiers placed in the front stages of the filters for amplifying the signals before noise is added thereto, as shown in FIG. 6.